solve simplify write the equation of the line that goes through (4,5) and is perpendicular to
TRANSCRIPT
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Solve 15 1 3 7
2x x
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211
x
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Simplify34
0 92
2x y x yy
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12
12
8xy
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Write the equation of the line that goes through
(4,5) and is perpendicular to 8 17x y
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8 27y x
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y varies directly with x and y is -3 when x is 6.
Write the equation.
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12
y x
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Solve2 7 33x
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15
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Write the inequality that matches this graph
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1x
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Solve
10 5 7 8x
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X = 1 and x = -2
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Simplify
2 03 4 9 7a b a b
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6
8
ab
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Which of the following numbers are rational and
real?2 0.61 153
0.72159..... 9 4i
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2 0.61 93
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Let f(x) and g(x) be the functions below and find (g-f)(x) in standard form
2
( ) 3 4
( ) 2 3
f x x
g x x x
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22 4x
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Let f(x) and g(x) be the functions below and find f(g(x))in standard form
2
( ) 3 4
( ) 2 3
f x x
g x x x
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26 9 4x x
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Let f(x) and g(x) be the functions below and find g(f(x))in standard form
2
10
( ) 2 5
f x x
g x x
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22 40 195x x
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Solve the system using substitution or elimination
7 5 132 3 17x yx y
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(4,3)
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How many solutions does the system below have?
Explain.3 2 66 4 8x yx y
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None. Show the lines are parallel (same slope and different y-intercept) or
attempt to solve the system and show you get nonsense.
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Rewrite the equation below to solve for C
32
A BC D
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6D ACB
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Determine the value of f(-3) for the function
22f x x x
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-15
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For what value(s) of x is the function defined? In other words, what is the domain of the function
below?
2
249
xf xx
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7x
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Express in standard form
2 5 6i i
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12 10i
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Write the inequality that matches this graph
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2 4y x
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What is the x-intercept, y-intercept, and the slope of
the line below?
2 4 16x y
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X-intercept: (8,0)Y-intercept: (0,4)Slope = m = -½
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Solve the inequality
4 2 1 3x
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52
x
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Which of the following is direct variation?
) 4) 7) 5
1) 32
A y xB yC x
D y x
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A
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Which of the following is a vertical line?
) 4) 7) 5
1) 32
A y xB yC x
D y x
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C
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Solve the proportion below. Please give an exact simplified answer.
2 1 14x
x
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1 334
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Find the equation for the inverse of the function below
1 62
f x x
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1 2 6 2 12f x x x
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Solve. Give exact simplified answers.
21 2 103x
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4 2x
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Solve the absolute value inequality below.
2 3 1 6x
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Make sure you can also graph the solution on a number line
1 4x
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It takes 4 hours to make an X and it costs $1. It takes 6 hours to make a Y an it costs $1. You have up to 24 hours available and up to $5 to spend on materials. You make a profit of $3 off an X and $2 off a Y. Your goal is to maximize profit
Write the constraints, graph the feasible region, write the objective function, and determine what will maximize profit.
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Constraints: x≥0, y ≥0, 4x+6y≤24, x+y ≤5Objective Function: P = 3x+2yCorner Points: (0, 0) (0, 4) (5, 0) (3, 2)Profit is maximized when x = 5 and y = 0
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Given the polynomial below and its given zero, determine
ALL of the zeros. 3 23 27 9
13
f x x x x
zero of x
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3x i
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Create a quartic polynomial in standard
form that has a repeated zero of 1 and a zero of
4 i
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4 3 26 2 26 17f x x x x x
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Reduce
11i
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i
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Algebraically find the vertex of the quadratic function below
3 1f x x x
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(1, -4)
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When is the function increasing?
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2
0
xandx
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Algebraically create the equation in standard form that matches this graph.
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3 23 4f x x x
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You are using 300 ft of fencing to create a pen for your horse on the side of your barn. The barn acts as one of the sides so you only fence on three sides. If x is the width of the pen, determine the following
The length in terms of x The area in terms of x How large x should be in order to
maximize the area for the horse
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2
300 2
2 30075
l x
A x xx ft
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If (-3, 5) is a point of f(x) then what point must be on ) ( 1) 7) 4 ( )a f xb f x
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a)(-4, -2)b)(3, 20)
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Determine the domain and range of the function below.
2 3 4y x
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Domain: {all real numbers}Range: { y≥4}
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Sketch a graph of the piecewise function
1 11 1
x if xf x
x if x
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A test has twenty questions worth 100 points. The test consists of True/False
questions worth 3 points each and multiple choice questions worth 11
points each. How many multiple choice questions and how many True/False questions are on the test? Assign
variables, write a system, and solve using substitution or elimination.
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5 multiple choice 15 True/False
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Solve the absolute value inequality below2 7 9 1x
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No Solution
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Solve3 28 4 2x x x
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1 50,4
x
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If a parabola contains the point (4, 7) and has an axis of
symmetry at x = 1, then based on symmetry what
other point must be on the parabola?
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(-2,7)
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Consider the functiona)Does it open up or down?b)Does it have a max or a min?c)What is the axis of symmetry?d)What is the vertex?e)What is the y-intercept?
22 1 3f x x
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Up Minimum x = 1 (1, 3) (0, 5) You should also be able to sketch the graph!
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Explain why the expression below is not a polynomial
function2 775 4 19.2y x ix x
x
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There is a non-real coefficient of 4i and there is a negative
power on the variable since 7 divided by x is equal
to 17x
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Write the equation of the line in slope-intercept form that
goes through these two points:
(-7, -1) and (5, 7)
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2 113 3
y x
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Simplify the expression below
21 2 3 2 4 65x y z x y z
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4
25x
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Which property is illustrated by-4 + 4 = 0
a) Associativeb) Commutative
c) Distributived) Identitye) Inverse
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Inverse property of addition
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Write the system of inequalities that matches this graph
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2 253 32
y x
y x
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Put into standard form4 71ii
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11 32 2
i
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Put into standard form 24 5 10 11 5 30i i i
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Good luck on your midyear exam. In addition to the review sheets, please spend time redoing your quizzes and
tests from first semester.
6 21i